The Search for Acceleration, part 3: Japan

June 26, 2013

CORRECTION: 6/30/13

The original detrended sea level rise rate graphs for this post was off by a factor of 12!. This greatly changes my conclusion. Incorrect information is now crossed out and is followed by corrected information in red.

Tide gauge data for the 20th century indicates that the average sea level rise rate was 1.8 mm/year. Satellite data from 1993 to present indicates a sea level rise rate of about 3 mm/year. This is part 3 of a series of posts looking for the acceleration necessary to reconcile those two facts

I am working under the theory that by detrending sea level data from individual (local) sites and averaging with other regional sites it should be possible to extract changes in regional rise rates while bypassing the question of what the “true” rise rate is for that region.

Japan

Conclusion: There is no convincing sign of a late century acceleration in the sea level rise rate in the tide gauge data from the Japan.

Conclusion: The rise rate during much of the satellite era has been much higher than the average for part of the 20th century for which data is available.

I looked for tide gauge data along the coast of Japan such that it covered at least the period from 1955 to 2008 with 90% of all monthly data accounted for. The following image shows the seven sites that met this criteria. The circles show a weighting threshold of 300 km.

Seven sites used in this analysis. Circles show 300 km weighting threshold

The following plot shows the qualifying data spread out for easy comparison. The key at the right shows the RLR data filenames.

Sea level data for all seven sites.

Data reduction and detrending

The following animation shows the transition through raw data, removal of the yearly signals, detrending, Gaussian smoothing and conversion to derivative (rise rate).

Here are the removed yearly signals and the weighting.

Yearly signals removed from Japanese RLR data

Number of files and effective weighting based on 300 km threshold.

Lets take a closer look at the detrended rise rate data and look for an acceleration in the satellite data era…

The very weak argument could be made that there was a rapid acceleration around 1985, but the resulting sea level rise rate was only about 0.25 mm/year higher than the average for the last half of the century. There was also an even greater acceleration around 1965, and sea level rise rate around 1970 was as high or higher than than in the 1990s. Finally, the 0.25 mm/year increase in the rise rate is only about 20% of the difference between the average global tide gauge rise rate for the 20th century (1.8 mm/year) and the satellite data (1993 to present) rise rate (about 3 mm/year).

So, I conclude that the Japanese data does not reconcile the difference between the 20th century tide gauge data and the satellite data.

The tide gauge data covering the part of the satellite data era (1993 to present) clearly shows a rise rate that is far greater than the average rise rate for the entire time period covered by the tide gauges. The period from 1993 to about 2003 may have a rise rate around 3 mm/year greater than the average, but after that the rise rate seems to fall again. Note that form about 1965 to 1975 the rise rate was also very high. This data from Japan does reconcile the difference between the satellite data and the average tide gauge data.

Fukushima

The following graphs show the sea level data from the Soma tide gauge station in Japan with the seven station shown above. Soma is the tide gauge station closest to the Fukushima nuclear reactors. The images speak for themselves.

2. Long-term tide gauge coverage of the coasts is much too sparse to derive a reliable global average. I compared long-term sea-level rise rates at all pairings of tide stations for which NOAA had fit a linear trend line, and found that only at distances less than about 800 km is there any increase in correlation at all, and only at distances less than 400 km is there a substantial increase in correlation between sea-level trends measured at pairs of tide stations.

3. Land movement (PGR/GIA, subsidence, etc.) affects coastal sea-level measurements differently from open-ocean sea-level. Theoretically, you could correct for that, but the widely-used model-derived Peltier adjustment factors for PGR are very rough estimates, only loosely correlated with reality.

4. But, most importantly, comparing coastal sea-levels, measured by tide stations, to open-ocean sea-levels, measured by satellites, is fundamentally a comparison between two very different quantities, like comparing apples to oranges.

Satellite measurements of sea level include thermal expansion. In fact, the IPCC estimates that thermal expansion accounts for about half of current & projected sea-level rise. But thermal expansion has almost no effect on coastal sea-levels and tide gauges measurements.

That might surprise you, but it should not surprise a physicist.

To understand how density changes in the upper ocean affect sea-level, remember Archimedes’ Principle, or consider the case of floating ice. The reason that an iceberg sticks up out of the ocean is that it has lower density than the water in which it floats. The amount of water that it displaces depends only on its mass, not on its density or shape.

Imagine an iceberg wrapped in a plastic bag. If it melts, its density increases, and the the exposed part that rises above the water sinks, but the volume of the iceberg below the surface does not change at all. If the iceberg in the plastic bag refreezes, it will rise up and protrude above the surface, but its displacement — the volume of seawater that it displaces — still will not change.

Because the amount of seawater that it displaces is unaffected by changes in its density, when it freezes/expands or thaws/contracts, it causes no lateral water flows. Only the localized elevation of its upper surface changes. It does not affect sea-level elsewhere.

Note that it is only the density of the floating object which matters, not whether it is solid, liquid, or slush. Displacement is measured in units of mass, and it isn’t affected by changes in density or solidity or shape.

The reason for that is that gravity balances mass, not volume. The same thing happens with density changes in liquid water. The upper layer of the ocean floats like an iceberg on top of the very cold water in the ocean depths, and there’s little mixing between them. When water in the upper layer of the ocean warms and expands, it rises up in place, like a very stubby iceberg. Gravity balances mass, not volume, so the thermal expansion causes no lateral water flows.

The exception to that rule is for water at the bottom of the ocean. If it expands, it has an effect similar to raising the ocean floor, which does cause lateral flows. But, in reality, that doesn’t happen at all in the deep ocean, where temperatures are extremely stable.

Almost all thermal expansion takes place in the upper layer of the ocean. Only a small portion of the ocean is shallow enough for warming to reach the water at the bottom and cause thermal expansion there. That means only a small portion of the ocean’s thermal expansion can cause lateral water flows and affect sea-level at the shorelines.

Without substantial lateral flows of water, there can be no significant effect on the coasts. Of course, temperature changes do affect the density of water at the shore, but that doesn’t cause the shoreline to advance or retreat. When water warms it gets deeper where it warms, by a (small) percentage of its depth. A percentage of zero is zero, so at the beaches, where the depth is near zero, the rise is negligible. Were that not the case, beaches would be wider and the shoreline would be further out to sea in the winter (when the water is cold) than in the summer (when the water is warm).

In summary, it is a mistake to compare satellite-measured deep-ocean sea-level rise to tide gauge-measured coastal sea-level rise. Even if the satellite data were trustworthy (which it isn’t), and even if we had perfectly accurate numbers for PGR/GIA corrections (which we don’t), and even if we also had accurate corrections for local subsidence (due to factors like groundwater extraction, oil & gas extraction, etc.), and even if we had comprehensive tide-gauge coverage of all the world’s coasts, it would still be a mistake to compare coastal sea-levels and deep-ocean sea-levels, because they are different quantities. Comparing them is like comparing apples to oranges.

You mention “The tide gauges are trustworthy; the satellites are not.”

My gut has always told me that this is correct. When I see good correlation between two or more tide gauges at different locations (but in the same region), that is an indication that something is being done right. It is also much easier for me to believe those correlated measurements that are done in situ are more accurate than remote sensing from a thousand kilometers away, with orbital uncertainty and decay and all kinds of other unexpected issues.

You also said “Long-term tide gauge coverage of the coasts is much too sparse to derive a reliable global average.”

Agreed. That is why I am bypassing any attempt to find a global average, or even regional averages of sea levels. When I detrend the data all hope of finding a regional sea level average is lost. And, the rise rates will be offset by constants. But the accelerations will be preserved. I am expressing this as “detrended rise rates.”

While detrending causes a loss of absolute rise rates, it allows for better averaging over time points or periods not covered by one or more data sets.

Again, my goal is to look for an acceleration at the end of the century, but I do not care that the rise rate is offset by some unknown constant.

You point out “Land movement (PGR/GIA, subsidence, etc.) affects coastal sea-level measurements differently from open-ocean sea-level. Theoretically, you could correct for that, but the widely-used model-derived Peltier adjustment factors for PGR are very rough estimates, only loosely correlated with reality.”

This is understood. I am making the rough assumption that these affects are more or less constant with time over the century at any particular location, and thus add a constant component to the rise rate at that location. But I am throwing out those constant components anyway when I detrend.

Your 4th point provides a greater challenge and will require more thought on my part. I will have to re-examine the relevance of my approach based on your comments.

I greatly appreciate your taking the time to make these detailed comments.